The diagnosis of a line or of an electrical cable by reflectometry is a well known method consisting in the injection of a wideband signal into the line and in the detection of the echoes, in order to track the variations of characteristic impedance of the line corresponding to irregularities, notably defects such as for example open circuits or short-circuits.
In its simplest version, the probe signal is a pulse whose duration depends on the bandwidth and of the length of the cable to be diagnosed.
Amongst the known reflectometry methods, the multicarrier reflectometry method known as MCTDR (Multi-Carrier Time-Domain Reflectometry) offers the advantage of being able to precisely control the spectrum of the injected signal and thus to be able to respond to imposed constraints on electromagnetic compatibility (EMC).
Henceforth, the following conventions will be adopted:
* denotes the convolution product
★ denotes the cross-correlation (inter-correlation)
h denotes the pulse response of the cable
ĥ denotes the estimated response of the cable: the reflectogram
x denotes the injected signal
y denotes the reflected signal
The notations in capitals denote the Fourier transforms of those in lower case
F{ } denotes the Fourier transform operation
F−1{ } denotes the inverse Fourier transform operation
The injected signal x and reflected signal y are linked via the following equation: y=x*h.
The aim of a reflectometry measurement is notably to measure the signal h, if possible with maximum precision.
h may be considered as a parsimonious signal, in other words it only contains peaks at the location of the irregularities on the cable.
In an ideal simplified case for a cable whose end is in open circuit, the difference in position between the first two peaks of h allows the knowledge of the length of the cable to be deduced.
When it is desired to monitor or diagnose a cable in use, at least one non-invasive measurement needs to be carried out, if it cannot be non-intrusive. Two conditions must then be met:
a suitable coupling means needs to be found, notably in terms of impedance;
signals having frequency components covering bands of frequencies already used in the target application must not be injected. In other words, any interference between the signals associated with the operation of the target application and the signals associated with the reflectometry is to be avoided, this leading to various constraints for the EMC, spectral occupation and robustness to noise.
The second condition notably allows the following double guarantee to be obtained:
the diagnostic signals do not interfere with those of the application in use, in transmission;
the signals of the application do not degrade the quality of the diagnosis, in terms of susceptibility.
By way of example:
for the diagnosis of an antenna cable for the application of an FM radio reception, the frequency band 88-108 MHz must be avoided for the diagnostic signal;
for the diagnosis of the CAN bus of a vehicle, the band 0.1-2 MHz must similarly be avoided.
The MCTDR technique, notably described in the patent application FR 2 931 323 A1, allows a probe signal to be constructed that meets a given spectral range requirement. The solution described can manage any given number of frequency bands with a variable attenuation coefficient within each band, which may go as far as total extinction.
However, in the solution described, an important technical limitation needs to be confronted. This is because, the more frequency bands are attenuated or suppressed, the poorer the abundance of the frequency content on the measurement of the reflected signal y, and the more the quality of the diagnosis is degraded.
In particular, if an ideal pulse were considered, represented by a Dirac function x=δ, for diagnosing the cable, h=y would be obtained. However, MCTDR is a pulse compression technique. In other words, the energy is not concentrated over a very short time period but distributed over the whole duration of the signal. It may be demonstrated mathematically, in this case, that: ĥ=Rxx*h, with Rxx=x★x, this auto correlation being called the pattern. The ideal case Rxx=δ is only possible if x contains all the frequencies. However, the more of the frequency components that are removed, the less the pattern resembles a pulse.
There exist several diagnostic techniques that do not interfere with a target application.
The reflectometry known as SSTDR (Spread Spectrum Time Domain Reflectometry) is a variant of STDR (Sequence Time Domain Reflectometry) reflectometry. STDR is also a pulse-compression technique. With this technique, instead of injecting a pulse, a binary sequence of square pulses, composed of +1 and −1, is injected into the cable in such a manner that the auto-correlation of the sequence is close to a pulse.
STDR does not allow the EMC constraints to be overcome but SSTDR provides an answer to this. For this purpose, the STDR sequence is modulated by a sinusoidal carrier of frequency f0. It is therefore, in fact, a modulated STDR sequence. In order to meet the operational constraints, f0 is chosen so as to move the modulated signal away from the forbidden bands.
A reflectometry method described in the document FR 2 931 323 A1 is an iterative method aiming to calculate h starting from the estimated pulse response ĥ. This is a post-processing algorithm which can take as input a reflectometry measurement made with a signal probe of the MCTDR type. It therefore benefits from being innocuous from the EMC point of view.
Multicarrier reflectometry, or MCR, uses the same waveforms as MCTDR, with a weighted sum of sinusoidal waves. For this reason, it provides the same quality of response to the EMC problems.
The processing of the reflected signal is however very different, since it uses an optimization algorithm (of the least-squares type) directly applied in the frequency domain in order to adapt the coefficients (α; τ) of a model of simplified parsimonious pulse response for the cable:
            h      ^        ⁡          (      t      )        =            ∑      i        ⁢                  α        i            ⁢              δ        ⁡                  (                      t            -                          2              ⁢              i              ⁢                                                          ⁢              τ                                )                    
This processing offers the advantage of being able to be carried out for a limited number of excitation frequencies.
The MCR technique is notably described in the article “Multicarrier Reflectometry”, IEEE SENSORS JOURNAL, VOL. 6, No. 3, June 2006.
One problem to be solved is notably to allow the flexibility of the injection methods with a controlled spectral width, such as notably MCTDR, while at the same time overcoming the problems of denaturation of the pattern which introduce a bias into the result of the diagnosis.
The reflectometry methods previously described do not solve this problem or solve it insufficiently.
SSTDR reflectometry seems to address this problem, but it does however have several drawbacks:                The modulation system around the frequency f0 introduces a complexity of implementation and additional costs.        It is complicated to change f0 “on the fly”, which does not allow a dynamic reconfiguration of the diagnostic system.        In certain applications, it may even be difficult to find an available frequency f0; it should be noted that the bandwidth of the cable is a limiting factor and f0 cannot be chosen to be arbitrarily high.        
Similarly, the algorithm described in the document FR 2 931 323 A1 for post-processing could be suitable. However, its robustness is compromised when peaks are located too close to one another in the pulse response h of the cable. Furthermore, it begins to converge in an erroneous manner when more than about one sixth (⅙) of the useful band of the test signal has been eliminated.
As far as the MCR method is concerned, although it appears to be insensitive to the cancelling of its coefficients, it suffers notably from the following prohibitive deficiencies:                Its use is limited to point-to-point cables.        It leads to an imprecision in localization which can reach 3% to 5% of the length of a cable.        